Viewing and display apparatus position determination algorithms

ABSTRACT

Celestial object location devices with sensor arrays of having less that one sensor for each of three orthogonal components of gravity and magnetic field vectors. The accuracy of position sensing is enhanced by estimating “missing” sensor input based on input from two orthogonal sensors provided, or determined with limitations from the two gravitational sensors provided.

This application is continuation of U.S. application Ser. No.11/376,670, filed Mar. 14, 2006, now U.S. Pat. No. 7,155,833, which is acontinuation of U.S. application Ser. No. 10/861,032 filed Jun. 4, 2004,now U.S. Pat. No. 7,010,862.

FIELD OF THE INVENTIONS

The inventions described below relate the field of astronomy,specifically to an electronic device capable of locating and identifyingcelestial objects.

BACKGROUND OF THE INVENTIONS

Norton, Viewing And Display Apparatus, U.S. Pat. No. 5,311,203 (May 10,1994) describes a viewing device for identifying features of interestwhich appear in the field of view of the device. Though Norton wasdescribed in the context of a hand-held star-gazing device, andpurported to provide information about asterisms (constellations orgroups of stars) in the field of view, the device does not work unlessheld with certain components held perfectly vertical during use. Anytwisting or rotation of the device about the viewing axis necessarilycauses errors, and introduces ambiguity that cannot be resolved. Thus,it is not possible to implement the Norton system, as proposed byNorton, in a hand-held device. Norton consists of a box-like housingwith a viewing channel therethrough, an LCD display and image overlaysystem for superimposing an image on the field of view, optics formanipulating the superimposed image to make it appear at infinity, asingle axis eccentrically weighted inclinometer to measure inclinationof the device and three magnetic sensors to determine the bearing of thedevice, a database with information regarding the constellations whichmight be viewed with the device, and a microprocessor. The viewingchannel establishes a field of view for the user, through which the usercan see constellations. The microprocessor is programmed to interpretsensor input and search the database for constellations in the field ofview, and transmit a reference display data to the display.

The Norton system suffers from crippling defects. An operational devicedepends on perfect vertical alignment of the inclinometer. Withoutperfect vertical alignment of the inclinometer the device cannotunambiguously determine its orientation. The slightest deviation fromvertical introduces ambiguity, such that the device can determine onlythat the viewing channel is aligned somewhere on a wide arc of the sky.If the device is not held perfectly vertically, that is, if it istwisted or rotated about the viewing axis, projection errors areintroduced into the output from the inclinometer, so that the device hasinadequate information regarding its inclination. In the case that thetwist induced error is small enough that the device can determine itsviewing axis with enough precision to generate a reference display thatcorresponds to constellations in the field of view, the device has noway to determine that it is twisted, and thus cannot rotate thereference display to align with the constellation.

Our own patents, Lemp, Celestial Object Location Device, U.S. Pat. No.6,366,212 (Apr. 2, 2002) and U.S. Pat. No. 6,570,506 (May 27, 2003) andour pending patent application Lemp, U.S. Publication 20030218546 (Nov.27, 2003) (the entirety of which is hereby incorporated by reference)provides solutions to this problem. Lemp shows a device for viewingcelestial objects from a location at a time and date ascertained by thedevice, comprising a viewing means to observe along a viewing axisdefined by an azimuth angle and a nadir angle or altitude; a processor,a multi-axis magnetic sensor adapted to provide the processor withazimuth data representing the azimuth angle, a multi-axis gravitationalsensor adapted to provide the processor with nadir data representing thenadir angle; location means for providing location data representing thelocation of the viewing device to the processor; time means forproviding time and date data representing the time and date to theprocessor; and a database adapted to be accessed by the processor andprovide data such that the processor determines celestial coordinates ofright ascension and declination corresponding to the viewing axis basedon the azimuth data, the nadir data, the location data, and the time anddate data. The device can be used to direct a user to a celestial object(its resolution is very high, so that it can direct the user toindividual stars and planets, as well as constellations and asterisms)and it can be used to identify an object to which the user has pointedthe device.

The position sensing function of the device is most accuratelydetermined using a three axis magnetic sensor and a three axisgravitational sensor. The use of lesser arrays will generally result inreduced accuracy and resolution of the device, such that it will bedesirable to improve the resolution with the methods described below,especially when the devices are embodied in celestial object locationdevices with magnifying optics.

SUMMARY

The devices and methods described below provide for enhanced accuracy ofposition sensing in a celestial object location device using sensorarrays of less than three axes. Information that would otherwise beprovided by a third axis gravitational sensor, for example, is obtainedby estimation based on input from the two gravitational sensorsprovided, or determined with limitations from the two gravitationalsensors provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a celestial object location device.

FIG. 2 illustrates the arrangement of the position sensor arrays inrelation to the viewing axis of the celestial object location device.

FIGS. 3 through 6 illustrate various transformations accomplished by thedevice microprocessor in calculating the nadir angle and azimuth angleof the device.

DETAILED DESCRIPTION OF THE INVENTIONS

FIG. 1 shows a celestial object location device (COL device) 10 is beingused by a user 12 to locate a celestial object 14. The COL device 10 hashousing 16 adapted to be hand-held. Other embodiments of the device mayor may not be hand-held. Non-limiting examples of such embodimentsnaturally include telescopes, binoculars, eyepieces, headpieces, and anymeans for viewing objects. The housing 16 of the COL device 10 has afirst view port 18 that is held proximate to the user 12 and a secondview port 20 proximate to the celestial object 14. During use, the viewports 18 and 20 are aligned between the user 12 and the celestial object14 and the COL device 10 is adapted such that the user views thecelestial object through the COL device along a viewing axis 34.Operation of the system is accomplished through one or moremicroprocessors operably connected to the sensors, a database, and userinput mechanisms, and outputs such as a side panel display, an aperturestop display, images superimposed on the field of view, imagescommunicated to a remote display, or audio segments played on a speakeror headphone or other suitable output means. The microprocessor mayprovide images or audio contents containing identifying data or locatinginstructions (as described in our U.S. Pat. No. 6,366,212, which ishereby incorporated by reference) to the output means.

FIG. 2 illustrates the arrangement of the position sensor arrays inrelation to the viewing axis of the celestial object location device. Amagnetic field sensor array 21 and a gravitational sensor array 22 aremounted on the housing 16, in fixed relationship to the viewing axis 34.The magnetic field sensor array 21 includes one magnetic sensor for eachaxis associated with a coordinate system defined relative to the deviceand its viewing axis. (This coordinate system is defined by the viewingaxis, a second axis perpendicular to the viewing axis and initiallyoriented upward relative to the ground when in use, and a third axisperpendicular to the first and second axes (initially parallel to theground). Though these axes may be conceived of as vertical or horizontalwhen considering the methods described herein, the tilting and twistingof the device in use will cause these axes to shift with no essentialrelationship to the terrestrial coordinate systems.) A first magneticfield sensor 21 x is aligned parallel to the viewing axis, and a secondmagnetic field sensor 21 y is arranged perpendicular to the firstsensor, and a third magnetic field sensor is aligned perpendicular tothe first and second magnetic field sensors, thus forming an array ofthree orthogonal magnetic sensors. The gravitation sensor array includesa first gravitational sensor 22 x arranged in parallel to the viewingaxis and a second gravitational sensor 22 y arranged perpendicular tothe first sensor. Gravitational sensor 22 y may be parallel or skewedparallel to the second magnetic field sensor 21 y. Each of the magneticfield sensors and gravitational sensors are operably connected to themicroprocessor to provide input to the microprocessor.

These arrays of sensors may be used to determine the direction in whichthe celestial object location is pointed, and the degree to which it istwisted about the viewing axis, within the typical viewing situations.The use of arrays with gravitational sensor arrays and/or magnetic fieldarrays with sensors oriented on less than three axes will generallyresult in reduced accuracy and resolution of the device, such thatimproved accuracy may be desired when the device is embodied incelestial object location devices with magnifying optics, and thedevices and methods described herein provide for enhanced accuracy ofposition sensing in a celestial object location device using sensorarrays of less than three axes. The new methods of calculating positionof a celestial object location device which incorporates only twogravitational sensors may be employed if one sensor involves estimatingthe missing third axis sensor via the magnitude of the existing two, andan estimate or calculation of the magnitude of the local gravity vector,from there it is similar to a full 3+3 system. The degree of errorencountered in the necessary calculations can be greatly reduced withthe algorithms described in the following paragraphs.

In the first method presented here, the missing component of the gravityinformation is calculated using the input from the existing sensors. Asinitial steps, the system is initialized, a process which includessystem startup and obtains position data and time data from appropriatesources (preferably GPS and its associated time signal and/or an onboardclock, though time and location can be manually input, or obtained fromsatellite broadcast time signals and alternative satellite ornavigational locating systems). The system then determines errorcorrection factors for sensor characteristics, such as alignment errors,temperature corrections, and other errors and biases. Some of thesesteps are performed at system startup and periodically during use.

Thereafter, the system receives and interprets input from the magneticfield sensor array and the gravitational sensor array. The algorithmfirst determines the nadir angle of the device by using thegravitational sensor array to calculate the gravity vector and itsrelationship to the viewing axis. To accomplish this, the systemreceives input from the gravitational sensors, and then estimates theinput from the “missing” gravitational sensor via an equation such asthe following:z=√{square root over (grav²−(x ² +y ²))}where z is the missing component, grav=estimated or calculated gravityfield magnitude for the current location (though the calculation canassume gravity equals one g in most cases, or resort to a more precisegravitational model where additional accuracy is desired), x is thevalue corresponding to the signal from the gravitational sensor which isparallel to sighting channel (item 22 x), and y is the valuecorresponding to the signal from the gravitational sensor which isperpendicular to sighting channel (item 22 y). With this information,the system determines the gravity vector, which is comprised of thedirection and magnitude of the sensed gravity.

Next, the system calculates a projection of the gravity vector onto thedevice—coordinate y-z plane. This step is illustrated in FIG. 3. Thisprovides the basis for determining the twist of the device in the nextstep.

Next, the system determines the “twist” of the device, which is therotation angle of the gravity vector (or its projection) about theviewing axis, using the y-axis as a starting point. To determine therotation angle, the microprocessor calculates the angle between thegravitational vector projection and the device y-axis (which isestablished by gravitational sensor 22 y).

Next, the system virtually “de-rotates” the device by rotating thegravity vector projection about the device x-axis by the rotation angle.This provides the basis for determining the nadir angle of the device,as that is the rotation of the device about its y-axis (which has beenrotated to match the local horizontal plane). This step is illustratedin FIG. 4.

Next, the system calculates the nadir angle of the rotated gravityvector projection, using the x-axis sensor.

With the nadir angle calculated, the system proceeds to use the input ofthe magnetic field sensors to determine the azimuth angle. This is doneby taking the magnetic field sensor input to calculate a magnetic fieldvector, and then transforming the magnetic field vector into horizoncoordinates (terrestrial coordinates defined relative to the earth'slocal horizontal plane). This is accomplished by virtually rotating themagnetic field vector about the device x-axis by the rotation angle.This is illustrated in FIG. 5. Next the rotated magnetic vector M isvirtually rotated around the device y-axis by the nadir angle to derivethe device orientation in the local magnetic field. This is illustratedin FIG. 6. This will orient the device such that its coordinate systemis correlated with the terrestrial coordinate system such that thedevice x-y plane is parallel to the terrestrial horizontal plane. Next,optionally, the system may refer to a magnetic model to ascertain thelocal dip angle and the expected magnitude of the magnetic field, andthis may be used to confirm that output of the magnetic sensors isreliable (this step is more fully described in our co-pending U.S.application Ser. No. 10/444,788, filed May 23, 2003, the entirety ofwhich is hereby incorporated by reference). Next, the resultant magneticvector is projected onto the local, terrestrial horizontal plane, andthe system calculates the azimuth angle (this allows the azimuth angledetermination to be independent of the dip angle). The azimuth angle iscalculated by determining the angle between projected magnetic vectorand device x-axis. Finally, the magnetic declination correction (thedifference between local magnetic north and true north) is used todetermine the actual azimuth angle.

With the azimuth angle and the nadir angle determined, the device knowswhere it is pointed in the sky, and can determine, as required by theuser input, what celestial objects appear in its field of view (for theidentify function) or where the user must be prompted, by appropriateoutput, to move the device to align the viewing axis with a desiredcelestial object (for the locate function).

In the second method of position sensing, rather than estimate a thirdaxis gravitational input, the system uses the gravitational sensorparallel to the viewing axis (22 x) to calculate the altitude, and usesthe gravitational sensor perpendicular to the sighting channel tocalculate device rotation. Once these two angles are read, calculationsproceed in a manner similar to a full 3-axis gravitational/3-axismagnetic field sensor system. Again, as initial steps, the system isinitialized, including system startup and obtaining position data andtime data from appropriate sources, and the system determines errorcorrection factors for sensor characteristics, such as alignment errors,temperature corrections, and other errors and biases.

Next, the system determines nadir angle on the basis of the input of thex-axis gravitational sensor 22 x, using an estimated or known localgravity magnitude (estimated gravity magnitude should be sufficient forhandheld devices with little or no magnification). The rotation angle ofthe device is then determined based on the output of y-axisgravitational sensor 22 y, which is perpendicular to the viewing axis.The step of estimating the third axis gravitational vector is not usedin this method.

Next, the system determines the azimuth angle as above. This includesdetermining the overall magnetic field vector M by combining the inputfrom the three magnetic field sensors 21 x, 21 y and 21 z, transformingthe magnetic field vector so that it is in terrestrial coordinates withan x-y plane parallel to the local ground plane, and completing thistransform to terrestrial coordinates by rotating this vector about thedevice y-axis by the rotation angle, and projecting this resultingvector onto the terrestrial x-y plane, and then determining the azimuthangle of the device by calculating the angel between the projectedvector and the device x-axis. Again, the system may optionally comparethe measured magnetic vector with the known local dip angle and theexpected magnitude of the magnetic field for correlation with a magneticmodel, and the system will preferably add a correction to the calculatedazimuth angle for the known magnetic declination correction (suitablecorrections techniques are disclosed in our co-pending U.S. applicationSer. No. 10/444,788).

For both methods, the system may make use of the known dip angle (whichis determined by the known terrestrial position and the magnetic modelstored in the database), and the measured magnetic field vector todetermine provide additional input to the nadir angle calculation. Inthis method, the system determines the nadir angle based on thegravitational sensors and the local vertical as established by thecomparison of the magnetic vector and the dip angle.

The method described above can be implemented with a variety ofgravitational sensors and magnetic field sensors. They can even beimplemented with inclinometers instead of gravitational sensors, thoughthe range in which the device can provide accurate location and identifyfunctionality may be limited. Also, the steps indicated above may beaccomplished in any appropriate order. Though the calculations have beendescribed in relation to linear algebra techniques suitable for theunderlying calculations, the calculations may be performed usingspherical trigonometry techniques (such techniques being equivalent tothe underlying linear algebra). The methods and devices may beincorporated into Celestial Object Location devices comprising scopeswith out optics or magnification, telescopes and binoculars, or anyother viewing means. Thus, while the preferred embodiments of thedevices and methods have been described in reference to the environmentin which they were developed, they are merely illustrative of theprinciples of the inventions. Other embodiments and configurations maybe devised without departing from the spirit of the inventions and thescope of the appended claims.

1. A method of viewing celestial objects comprising the steps: providinga celestial object viewing device having a viewing axis defined by anazimuth angle and a nadir angle, a magnetic field sensor array having afirst, second and third magnetic field sensors arranged orthogonallywith the first magnetic field sensor aligned parallel to the viewingaxis and each magnetic field sensor generating a signal proportional toa sensed magnetic field, a gravitational sensor array having twoperpendicular gravity sensors, with a first gravity sensor alignedparallel to the viewing axis and each gravity sensor generating a signalproportional to a sensed gravity field, a microprocessor, a database,and output means; the microprocessor receiving signals from the magneticfield sensors and the gravity field sensors; the microprocessorcomputing an azimuth angle and a nadir angle relative to the viewingaxis; the microprocessor providing data from the database to the outputmeans related to celestial objects aligned with the viewing axis.
 2. Themethod of claim 1 wherein the microprocessor computing step furthercomprises the steps: determining a first gravity field component fromthe first gravity field sensor; determining a second gravity fieldcomponent from the gravity field sensor perpendicular to the firstgravity field sensor; computing a third gravity field component usingthe first and second gravity field components; computing the nadir angleusing the first, second and third gravity field components.
 3. Themethod of claim 1 wherein the microprocessor computing step furthercomprises the steps: determining a first magnetic field component fromthe first magnetic field sensor; determining a second magnetic fieldcomponent from the second magnetic field sensor; determining a thirdmagnetic field component from the third magnetic field sensor; computingthe azimuth angle using the first, second and third magnetic fieldcomponents.
 4. A celestial viewing device comprising: a housing defininga viewing axis forming an azimuth angle and a nadir angle; a magneticsensor array in the housing, the magnetic sensor array having a first,second and third magnetic field sensors arranged orthogonally with thefirst magnetic field sensor aligned parallel to the viewing axis andeach magnetic field sensor operable to produce a magnetic signalproportional to a sensed magnetic field; a gravitational sensor array inthe housing, the gravitational sensor array having two perpendiculargravity sensors, with a first gravity sensor aligned parallel to theviewing axis and each gravity sensor operable to produce a gravitysignal proportional to a sensed gravity field; a database; output meansfor presenting data to a user; and a microprocessor operable to receivethe magnetic signals and compute the azimuth angle relative to theviewing axis, and receive the gravity signals and compute the nadirangle relative to the viewing axis, and interact with the database toprovide data to the output means related to the viewing axis.
 5. Theapparatus of claim 4 wherein the microprocessor further comprises: amicroprocessor operable to determine a first gravity field componentfrom the first gravity field sensor signal, and determine a secondgravity field component from the gravity signal of the gravity fieldsensor perpendicular to the first gravity field sensor, and compute athird gravity field component using the first and second gravity fieldcomponents and compute the nadir angle relative to the viewing axisusing the first, second and third gravity field components, receive themagnetic signals and compute the azimuth angle relative to the viewingaxis, and interact with the database to provide data to the output meansrelated to the viewing axis.
 6. The apparatus of claim 4 wherein themicroprocessor further comprises: a microprocessor operable to determinea first magnetic field component from the first magnetic field sensor,to determine a second magnetic field component from the second magneticfield sensor, to determine a third magnetic field component from thethird magnetic field sensor, to compute the azimuth angle using thefirst, second and third magnetic field components, and receive thegravity signals and compute the nadir angle relative to the viewingaxis, and interact with the database to provide data to the output meansrelated to the viewing axis.
 7. The apparatus of claim 4 wherein themicroprocessor further comprises: a microprocessor operable to determinea first gravity field component from the first gravity field sensorsignal, and determine a second gravity field component from the gravitysignal of the gravity field sensor perpendicular to the first gravityfield sensor, and compute a third gravity field component using thefirst and second gravity field components and compute the nadir anglerelative to the viewing axis using the first, second and third gravityfield components, the microprocessor operable to determine a firstmagnetic field component from the first magnetic field sensor, todetermine a second magnetic field component from the second magneticfield sensor, to determine a third magnetic field component from thethird magnetic field sensor, to compute the azimuth angle using thefirst, second and third magnetic field components, and themicroprocessor operable interact with the database to provide data tothe output means related to the viewing axis.
 8. A method of viewingcelestial objects comprising the steps: providing a celestial objectviewing device having a viewing axis defined by an azimuth angle and anadir angle, a magnetic field sensor array having a first, second andthird magnetic field sensors arranged orthogonally with the firstmagnetic field sensor aligned parallel to the viewing axis and eachmagnetic field sensor generating a signal proportional to a sensedmagnetic field, a gravitational sensor array having two perpendiculargravity sensors, with a first gravity sensor aligned parallel to theviewing axis and each gravity sensor generating a signal proportional toa sensed gravity field, a microprocessor, a database, and output means;the microprocessor receiving signals from the magnetic field sensors andthe gravity field sensors; the microprocessor computing an azimuth angleand a nadir angle relative to the viewing axis.
 9. The method of claim 8wherein the microprocessor computing step further comprises the steps:determining a first gravity field component from the first gravity fieldsensor; determining a second gravity field component from the gravityfield sensor perpendicular to the first gravity field sensor; computinga third gravity field component using the first and second gravity fieldcomponents; computing the nadir angle using the first, second and thirdgravity field components.
 10. The method of claim 8 wherein themicroprocessor computing step further comprises the steps: determining afirst magnetic field component from the first magnetic field sensor;determining a second magnetic field component from the second magneticfield sensor; determining a third magnetic field component from thethird magnetic field sensor; computing the azimuth angle using thefirst, second and third magnetic field components.
 11. A celestialviewing device comprising: a housing defining a viewing axis forming anazimuth angle and a nadir angle; a magnetic sensor array in the housing,the magnetic sensor array having a first, second and third magneticfield sensors arranged orthogonally with the first magnetic field sensoraligned parallel to the viewing axis and each magnetic field sensoroperable to produce a magnetic signal proportional to a sensed magneticfield; a gravitational sensor array in the housing, the gravitationalsensor array having two perpendicular gravity sensors, with a firstgravity sensor aligned parallel to the viewing axis and each gravitysensor operable to produce a gravity signal proportional to a sensedgravity field; output means for presenting data to a user; and amicroprocessor operable to receive the magnetic signals and compute theazimuth angle relative to the viewing axis, and receive the gravitysignals and compute the nadir angle relative to the viewing axis, andprovide data to the output means related to the viewing axis.
 12. Theapparatus of claim 11 wherein the microprocessor further comprises: amicroprocessor operable to determine a first gravity field componentfrom the first gravity field sensor signal, and determine a secondgravity field component from the gravity signal of the gravity fieldsensor perpendicular to the first gravity field sensor, and compute athird gravity field component using the first and second gravity fieldcomponents and compute the nadir angle relative to the viewing axisusing the first, second and third gravity field components, receive themagnetic signals and compute the azimuth angle relative to the viewingaxis, and interact with the database to provide data to the output meansrelated to the viewing axis.
 13. The apparatus of claim 11 wherein themicroprocessor further comprises: a microprocessor operable to determinea first magnetic field component from the first magnetic field sensor,to determine a second magnetic field component from the second magneticfield sensor, to determine a third magnetic field component from thethird magnetic field sensor, to compute the azimuth angle using thefirst, second and third magnetic field components, and receive thegravity signals and compute the nadir angle relative to the viewingaxis, and interact with the database to provide data to the output meansrelated to the viewing axis.
 14. The apparatus of claim 11 wherein themicroprocessor further comprises: a microprocessor operable to determinea first gravity field component from the first gravity field sensorsignal, and determine a second gravity field component from the gravitysignal of the gravity field sensor perpendicular to the first gravityfield sensor, and compute a third gravity field component using thefirst and second gravity field components and compute the nadir anglerelative to the viewing axis using the first, second and third gravityfield components, the microprocessor operable to determine a firstmagnetic field component from the first magnetic field sensor, todetermine a second magnetic field component from the second magneticfield sensor, to determine a third magnetic field component from thethird magnetic field sensor, to compute the azimuth angle using thefirst, second and third magnetic field components, and themicroprocessor operable interact with the database to provide data tothe output means related to the viewing axis.